Is this mentioned in authoritative sources that I can cite?
–
Michael HardyNov 2 '12 at 18:26

I can be pretty authoritative myself if that's what you need :). Honestly, I have no idea. Probably yes, but if I were writing a paper and needed this fact, I would just include the line I wrote as an answer and not bother about any citations. Indeed, what's the point of sending the reader to the library if you can tell the whole story in one line?
–
fedjaNov 3 '12 at 0:13

What I might do is write a paper in which I mention in passing the fact that if $x_1+x_2+x_3+\cdots$ converges absolutely then so do the two series I asked about, but that I prefer not to rely on that, but instead to do something else. So a one-line comment might be just what I need.
–
Michael HardyNov 3 '12 at 2:45